Mitt Romney handed Barack Obama a potential gift for the US presidential election campaign when the presumptive Republican nominee blundered on his first diplomatic outing by questioning whether London was capable of staging a successful Olympic Games.

In a move that astonished Downing Street, hours before it laid on a special reception for Romney at No 10, he told NBC there were "disconcerting" signs about the preparations for the Games. One senior Whitehall source said: "What a total shocker. We are speechless."

David Cameron wasted no time in rebuking Romney hours after his remarks were broadcast. On a visit to the Olympic Park, the prime minister said: "We are holding an Olympic Games in one of the busiest, most active, bustling cities in the world. Of course it's easier if you hold an Olympic Games in the middle of nowhere."

Cameron's remarks were intended to be a light-hearted jibe at Romney, who used his famous management skills honed at Bain Capital to rescue the 2002 Winter Olympics in Salt Lake City, Utah.

Boris Johnson, the London mayor, joined in the jibes at a celebration to greet the Olympic torch in Hyde Park. "I hear there's a guy called Mitt Romney who wants to know whether we're ready," Johnson yelled from the stage to a cheering crowd.

"He wants to know whether we're ready. Are we ready? Are we ready? Yes, we are."

Romney rowed back after a 45-minute meeting in Downing Street where the prime minister expressed his unease about his remarks. "I am very delighted with the prospects of a highly successful Olympic Games. What I have seen shows imagination and forethought and a lot of organisation and [I] expect the Games to be highly successful," he said.

When asked about the preparations for the Olympics in an interview on Wednesday night with the NBC anchor Brian Williams, Romney said: "There are a few things that were disconcerting, the stories about the private security firm not having enough people, supposed strike of the immigration and customs officials, that obviously is not something which is encouraging. Because there are three parts that makes Games successful.

"Number one, of course, are the athletes. That's what overwhelmingly the Games are about. Number two are the volunteers. And they'll have great volunteers here. But number three are the people of the country. Do they come together and celebrate the Olympic moment? And that's something which we only find out once the Games actually begin."

In Washington, Democrats pounced on the comments. Harry Reid, the majority leader in the Senate, said they were an embarassment for the US. "It's not good for us as a country – it's not good for him – but as a country to have somebody that's nominated by one of the principal parties to go over and insult everybody," Reid told the Huffington Post.

Romney's campaign team set up a conference call with US reporters in an attempt to limit the damage from the faltering UK visit. The campaign fielded Lousiana governor Bobby Jindal and Virginia governor Bob McDonnell in Romney's defence. "We're not worried about overseas headlines. We're worried about voters back here in America," Jindal said in comments reported by Talking Points Memo.

The Olympics blunder came on top of what had been an inauspicious start to Romney's week-long overseas trip, designed in part to establish his foreign policy credentials with voters back home. His camp was forced to repudiate comments by an un-named adviser who told the Daily Telegraph that Barack Obama, the first black US president, had mishandled Anglo-American ties and that Romney better understood the "Anglo-Saxon heritage" between the two countries.

On Thursday, Romney also took the unusual step of acknowledging that he had met the head of MI6, Britain's secretive foreign intelligence agency, when asked about his discussions with British officials about Syria. Such conversations are not normally discussed publicly by government leaders.

"I can only say that I appreciated the insights and the perspectives of the leaders of the government here and opposition here as well as the head of MI6 as we discussed Syria and hoped for a more peaceful future for that country," he said.

Romney also met Ed Miliband, the leader of the oppositon Labour party. Miliband took questions from two reporters from what he called "my side", but Romney would not take questions from US journalists. At one point, Romney called Miliband "Mr Leader", which prompted suggestions he had forgotten Miliband's name.

There were also meetings with foreign secretary William Hague, deputy prime minister Nick Clegg and former PM Tony Blair.

Romney later went on to a fundraiser at the Mandarin hotel in London, at which he repeated his promise to restore a bust of Winston Churchill to the Oval Office in the White House if he is elected. Obama replaced the bust with one of Abraham Lincoln after his election, in what was interpreted in the British media as a snub to the transatlantic relationship.

His campaign team claimed the event took $2m in donations, but there were reports earlier that ticket prices had been lowered, and that some people had been offered free passes.